[@Raineh Daze]
No limit to supply?

Wasn't it a plot point in GX that LiNKER supplies were low owing to the fact that the one of the two people who can make it, Ryoko was dead (not to mention was the reincarnated personality of a lustful ancient priestess) and the other one is sealed away in an underwater black box... Vercingetorix would later die when he goes literally Handsome Jack...

Or are we handwaving it that Carol/Elfnein considering she's an Alchemist can make LiNKER by being really smart... We still run into the problem of logistics since if she could make LiNKER we still have the problem of needing it to go from the world of Symphogear to Lydia's place. 

This be why I was thinking that they might be AU even though the players didn't specify it since We've only ever seen Miku use her Symphogear once (Is it even hers? is a relic even the property of the lady using it?) and that was her high on drugs.